Capabilities

Overview

• Support for a wide array of types of optimisation problems (continuous, integer, single and multi-objective, constrained and unconstrained, with or without derivatives, stochastic, etc.).

• A comprehensive library of algorithms, including global and local solvers, meta-heuristics, single and multi-objective algorithms, wrappers for third-party solvers (e.g., NLopt, Ipopt, SciPy, etc.).

• Comprehensive support for coarse-grained parallelisation via the generalised island model. In the island model, multiple optimisation instances run in parallel (possibly on different machines) and exchange information as the optimisation proceeds, improving the overall time-to-solution and allowing to harness the computational power of modern computer architectures (including massively-parallel high-performance clusters).

• Support for fine-grained parallelisation (i.e., at the level of single objective function evaluations) in selected algorithms via the batch fitness evaluation framework. This allows to speed-up single optimisations via parallel processing (e.g., multithreading, high-performance clusters, GPUs, SIMD vectorization, etc.).

• A library of ready-to-use optimisation problems for algorithmic testing and performance evaluation (Rosenbrock, Rastrigin, Lennard-Jones, etc.).

• A library of optimisation-oriented utilities (e.g., hypervolume computation, non-dominated sorting, plotting, etc.).

List of algorithms

This is the list of user defined algorithms (UDAs) currently provided with pygmo. These are classes that can be used to construct a pygmo.algorithm, which will then provide a unified interface to access the algorithm’s functionalities.

Generally speaking, algorithms can solve only specific problem classes. In the tables below, we use the following flags to signal which problem types an algorithm can solve:

• S = Single-objective

• M = Multi-objective

• C = Constrained

• U = Unconstrained

• I = Integer programming

• sto = Stochastic

Note that algorithms that do not directly support integer programming will still work on integer problems (i.e., they will optimise the relaxed problem). Note also that it is possible to use meta-problems to turn constrained problems into unconstrained ones, and multi-objective problems into single-objective ones.

Heuristic Global Optimization

Common Name	Docs of the python class	Capabilities
Extended Ant Colony Optimization (GACO)	pygmo.gaco	S-CU-I
Differential Evolution (DE)	pygmo.de	S-U
Self-adaptive DE (jDE and iDE)	pygmo.sade	S-U
Self-adaptive DE (de_1220 aka pDE)	pygmo.de1220	S-U
Grey wolf optimizer (GWO)	pygmo.gwo	S-U
Improved Harmony Search	pygmo.ihs	SM-CU-I
Particle Swarm Optimization (PSO)	pygmo.pso	S-U
Particle Swarm Optimization Generational (GPSO)	pygmo.pso_gen	S-U-sto
(N+1)-ES Simple Evolutionary Algorithm	pygmo.sea	S-U-sto
Simple Genetic Algorithm	pygmo.sga	S-U-I-sto
Corana’s Simulated Annealing (SA)	pygmo.simulated_annealing	S-U
Artificial Bee Colony (ABC)	pygmo.bee_colony	S-U
Covariance Matrix Adaptation Evo. Strategy (CMA-ES)	pygmo.cmaes	S-U-sto
Exponential Evolution Strategies (xNES)	pygmo.xnes	S-U-sto
Non-dominated Sorting GA (NSGA2)	pygmo.nsga2	M-U-I
Multi-objective EA with Decomposition (MOEA/D)	pygmo.moead	M-U
Multi-objective EA with Decomposition Generational (GMOEA/D)	pygmo.moead_gen	M-U
Multi-objective Hypervolume-based ACO (MHACO)	pygmo.maco	M-U-I
Non-dominated Sorting PSO (NSPSO)	pygmo.nspso	M-U

Local optimization

Common Name	Docs of the python class	Capabilities
Compass Search (CS)	pygmo.compass_search	S-CU
COBYLA (from NLopt)	pygmo.nlopt	S-CU
BOBYQA (from NLopt)	pygmo.nlopt	S-U
NEWUOA + bound constraints (from NLopt)	pygmo.nlopt	S-U
PRAXIS (from NLopt)	pygmo.nlopt	S-U
Nelder-Mead simplex (from NLopt)	pygmo.nlopt	S-U
Subplex (from NLopt)	pygmo.nlopt	S-U
MMA (Method of Moving Asymptotes) (from NLopt)	pygmo.nlopt	S-CU
CCSA (from NLopt)	pygmo.nlopt	S-CU
SLSQP (from NLopt)	pygmo.nlopt	S-CU
Low-storage BFGS (from NLopt)	pygmo.nlopt	S-U
Preconditioned truncated Newton (from NLopt)	pygmo.nlopt	S-U
Shifted limited-memory variable-metric (from NLopt)	pygmo.nlopt	S-U
Nelder-Mead simplex (from SciPy)	pygmo.scipy_optimize	S-U
Powell (from SciPy)	pygmo.scipy_optimize	S-U
CG (from SciPy)	pygmo.scipy_optimize	S-U
BFGS (from SciPy)	pygmo.scipy_optimize	S-U
Low-storage BFGS (from SciPy)	pygmo.scipy_optimize	S-U
COBYLA (from SciPy)	pygmo.scipy_optimize	S-CU
SLSQP (from SciPy)	pygmo.scipy_optimize	S-CU
Trust Constr (from SciPy)	pygmo.scipy_optimize	S-CU
Dogleg (from SciPy)	pygmo.scipy_optimize	S-U
Trust Ncg (from SciPy)	pygmo.scipy_optimize	S-U
Trust exact (from SciPy)	pygmo.scipy_optimize	S-U
Trust Krylov (from SciPy)	pygmo.scipy_optimize	S-U
Ipopt	pygmo.ipopt	S-CU
SNOPT (in pagmo_plugins_non_free affiliated package)	pygmo.snopt7	S-CU
WORHP (in pagmo_plugins_non_free affiliated package)	pygmo.wohrp	S-CU

Meta-algorithms

Common Name	Docs of the python class	Capabilities 1
Monotonic Basin Hopping (MBH)	pygmo.mbh	S-CU
Cstrs Self-Adaptive	pygmo.cstrs_self_adaptive	S-C
Augmented Lagrangian algorithm (from NLopt) 2	pygmo.nlopt	S-CU

Footnotes

1

The capabilities of the meta-algorithms depend also on the capabilities of the algorithms they wrap. If, for instance, a meta-algorithm supporting constrained problems is constructed from an algorithm which does not support constrained problems, the resulting meta-algorithms will not be able to solve constrained problems.

2

The Augmented Lagrangian algorithm can be used only in conjunction with other NLopt algorithms.

List of problems

This is the list of user defined problems (UDPs) currently provided with pygmo. These are classes that can be used to construct a pygmo.problem, which will then provide a unified interface to access the problem’s functionalities.

In the tables below, we classify optimisation problems according to the following flags:

• S = Single-objective

• M = Multi-objective

• C = Constrained

• U = Unconstrained

• I = Integer programming

• sto = Stochastic

Scalable problems

Common Name	Docs of the python class	Type
Ackley	pygmo.ackley	S-U
Golomb Ruler	pygmo.golomb_ruler	S-C-I
Griewank	pygmo.griewank	S-U
Hock schittkowski 71	pygmo.hock_schittkowski_71	S-C
Inventory	pygmo.inventory	S-U-sto
Lennard Jones	pygmo.lennard_jones	S-U
Luksan Vlcek 1	pygmo.luksan_vlcek1	S-C
Rastrigin	pygmo.rastrigin	S-U
MINLP Rastrigin	pygmo.minlp_rastrigin	S-U-I
Rosenbrock	pygmo.rosenbrock	S-U
Schwefel	pygmo.schwefel	S-U

Problem suites

Common Name	Docs of the python class	Type
CEC2006	pygmo.cec2006	S-C
CEC2009	pygmo.cec2009	S-C
CEC2013	pygmo.cec2013	S-U
CEC2014	pygmo.cec2014	S-U
ZDT	pygmo.zdt	M-U
DTLZ	pygmo.dtlz	M-U
WFG	pygmo.wfg	M-U

Meta-problems

Meta-problems are UDPs that take another UDP as input, yielding a new UDP which modifies the behaviour and/or the properties of the original problem in a variety of ways.

Common Name	Docs of the python class
Decompose	pygmo.decompose
Translate	pygmo.translate
Unconstrain	pygmo.unconstrain
Decorator	pygmo.decorator_problem
Constant Arguments	pygmo.constant_arguments

List of islands

This is the list of user defined islands (UDIs) currently provided with pygmo. These are classes that can be used to construct a pygmo.island, which will then provide a unified interface to access the island’s functionalities.

In the pygmo jargon, an island is an entity tasked with managing the asynchronous evolution of a population via an algorithm in the generalised island model. Different UDIs enable different parallelisation strategies (e.g., multithreading, multiprocessing, cluster architectures, etc.).

Common Name	Docs of the python class
Thread island	pygmo.thread_island
Multiprocessing island	pygmo.mp_island
Ipyparallel island	pygmo.ipyparallel_island

List of batch fitness evaluators

This is the list of user defined batch fitness evaluators (UDBFEs) currently provided with pygmo. These are classes that can be used to construct a pygmo.bfe, which will then provide a unified interface to access the evaluator’s functionalities.

In the pygmo jargon, a batch fitness evaluator implements the capability of evaluating a group of decision vectors in a parallel and/or vectorised fashion. Batch fitness evaluators are used to implement fine-grained parallelisation in pygmo (e.g., parallel initialisation of populations, or parallel fitness evaluations within the inner loop of an algorithm).

Common Name	Docs of the python class
Default BFE	pygmo.default_bfe
Thread BFE	pygmo.thread_bfe
Member BFE	pygmo.member_bfe
Multiprocessing BFE	pygmo.mp_bfe
Ipyparallel BFE	pygmo.ipyparallel_bfe